Magnetic Forces on Wires and Charges

With permanent magnets opposite poles attract and like poles repel. As we have seen magnetic fields surround any current carrying wire. Therefore it stands to reason that magnetic forces will act on wires carrying electric current and charged particles moving in a magnetic field.

Parallel Current Carrying Wires Picture two parallel wires carrying current in the same direction, would the fields produced by these wires attract or repel? Parallel wires with current flowing in the same direction will attract each other.

The same logic can be used to determine how parallel wires containing currents the flow in the opposite direction interact. Parallel wires with current flowing in the opposite directions will repel.

Current Carrying Wires in Magnetic Fields A current carrying wire in a magnetic field will also experience a force. Imagine a current carrying wire placed between two permanent magnets. S N X S N

Note that above the wire both the permanent magnetic field and the field generated by the wire point in the same direction These two fields will repel. Also, below the wire the permanent magnetic field and the field generated by the wire point in opposite directions. These two fields will attract.

Thumb: Particle Motion/ Current The 3rd Right Hand Rule: Thumb: Particle Motion/ Current Index Finger: Magnetic Field Palm: Force

The magnitude of the magnetic force on a conductor can be calculated as: Where: B = I = l = θ = F = BIlsinƟ

Note that if the conductor is perpendicular to the magnetic field this formula becomes: F = BIl Because sin(90o) = 1 If the conductor is parallel to the magnetic field then there is no magnetic force acting on it.

Moving Charges in Magnetic Fields In the same way that charged particles moving through a wire will experience a force in a magnetic field, so will free charged particles. To determine the direction of the force on such a particle we simply use the RHR.

Moving Charges in Magnetic Fields NOTE: We use the right hand rules for wires when talking about conventional current And the left hand rules for wires when talking about electron flow.

Moving Charges in Magnetic Fields We follow the same logic when dealing with charged particles: For positive particles use RHR For negative particles use LHR

NOTE: Just like the magnetic force on conductors this formula can be reduced to   when the particles are moving perpendicular to the magnetic field. F = qvB To calculate the magnetic force on the particle we use: Where: q = v = B = θ = F = qvBsinƟ

If a charged particle enters a magnetic field traveling perpendicular to the field, it will deflect continuously and travel in a circle. Consider an electron moving through a magnetic field X X X X X X X X X X X X X X X X

Now consider a proton moving through the same magnetic field X X X X X X X X X X X X X X X X